Nonlinear Differential Problems with Smooth and Nonsmooth Constraints - 1st Edition - ISBN: 9780128133866

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

1st Edition

Authors: Dumitru Motreanu
Paperback ISBN: 9780128133866
Imprint: Academic Press
Published Date: 1st June 2018
Page Count: 304
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Table of Contents

1. Prerequisites of functional analysis and operator theory
2. Prerequisites of regularity theory and maximum principle
3. Nonlinear elliptic eigenvalue problems
4. Nonlinear elliptic equations with general dependence on the solution gradient
5. Constant sign and sign-changing solutions for quasilinear elliptic problems
6. Nonlinear elliptic systems
7. Singular quasilinear elliptic systems
8. Evolutionary variational and quasivariational inequalities
9. Control problems for evolutionary differential inclusions


Description

This research monograph systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is to a large extent self-contained and requires only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by numerous end-of-chapter problems and hundreds of carefully curated references.

Key Features

  • Builds progressively from functional analysis and operator theory to nonlinear elliptic systems and control problems
  • Outlines the evolution of the main ideas of nonlinear analysis, and their roots in classical mathematics
  • Presented with numerous end-of-chapter exercises and sophisticated open problems
  • Illustrated with pertinent industrial and engineering numerical examples and applications
  • Accompanied by hundreds of curated references, saving researchers hours of research in conducting literature analysis

Readership

Primarily early career researchers at PhD level in functional, nonlinear and non-smooth analysis with experience in functional analysis and general topology. Some researchers studying relatable mathematical problems in mechanics, physics, engineering and biology


Details

No. of pages:
304
Language:
English
Copyright:
© Academic Press 2018
Published:
Imprint:
Academic Press
Paperback ISBN:
9780128133866

About the Authors

Dumitru Motreanu Author

Dumitru Motreanu is Professor of Mathematics at the University of Perpignan, France. Dr. Motreanu received the Ph.D. degree in 1978 from the University of Iasi, Romania. In 1991 he was a recipient of Simeon Stoilov Award from the Romanian Academy of Sciences. His areas of expertise cover partial differential equations and nonlinear analysis. He obtained original results in smooth and nonsmooth variational methods, nonlinear eigenvalue problems, multiple solutions for elliptic equations and systems. He coauthored 7 monographs in mathematics and published more than 190 professional articles in prestigious international journals of mathematics as well as more than 20 chapters in research volumes. He also edited a handbook of nonconvex analysis and three special issues of international journals. His results are cited and used in more than 1900 refereed papers. He serves in the editorial boards of more than 20 academic journals in mathematics.

Affiliations and Expertise

Department of Mathematics, University of Perpignan, Perpignan, France